Talk:Derivative at a point

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Revision as of 19:54, 21 January 2011 by imported>Peter Schmitt (→‎Derivative: explanation)
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 Definition:  The local rate of change of a function with respect to its argument. [d] [e]
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Derivative

Peter, could you please explain why you prefer the title "differential quotient"? I haven't studied mathematics in English for some time, but I still feel that "derivative" is the more common name. Formally, the derivative should be the limit of the differential quotient as h approaches zero, but in my mind they are not the same concept. Johan A. Förberg 22:08, 21 January 2011 (UTC)

I see a subtle difference:
  • The differential quotient of f at x is the limit of the difference quotients at x (only one particular point considered),
  • while the derivative of f is the function with values equal to the differential quotient (the full dominion of the function is considered).
(The redirect is not final, "derivative" should have its own page, as should have "derivation".)
Peter Schmitt 00:54, 22 January 2011 (UTC)
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